Interest rate data were obtained from two sources. The Bank for International Settlements provided daily 3-, 6-, and 12-month Eurocurrency deposit rates for 21 countries, collected around 10 AM Swiss time. The data begin on January 3, 1977 for five currencies (German mark, Dutch guilder, Swiss franc, pound, and U.S. dollar), on September 1, 1977 for most other currencies, and run through August 31, 1998.
Swap rate data were downloaded from Datastream for nine European countries. Swap rates are the European coupon rates in a semiannual exchange of fixed European interest payments against floating dollar interest rate payments indexed to the Eurodollar interest rate; principal is also exchanged at maturity. Since the dollar floating-rate cash flows are at par at the swap’s inception, swap rates provide the European coupon rate such that a European bond with semiannual coupons would be at par — or, equivalently, the European semiannual yields to maturity, times two. Swap rate data are more readily available than country-specific bond yields. As with other Euromarket data, swap rates also alleviate concerns about country-specific default risk, capital controls, and tax issues, as well as eliminating heterogeneity across national data sources.
Midpoint swap rates were used; the average of bid and ask. Swap rates for 2-5, 7, and 10-year maturities were available for all countries except Denmark and Sweden beginning on June 24, 1991. Danish swap rates began on February 25, 1993, while Swedish rates began on January 2, 1992. Data for 1-, 6-, 8-, and 9-year maturities began on November 15 or 16, 1994 for all countries except France. French franc 1-year swap rates began on October 31, 1994, while 6-, 8-, and 9-year maturities began on January 24, 1995. Weekly (Wednesday) observations were selected from the daily data, with the nearest other day used when Wednesday was a holiday.
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The 3- and 6-month forward rates used in testing the expectations hypothesis in section II.B were
where yt, A, and ut are Nx 1, zt and vt are K x 1, ^ is an N x N matrix assumed diagonal and nonnegative, Q is a K x K positive semidefinite matrix, and N> K. (A.6) is underidentified, since any transformation of the underlying state vector(e.g., xt 9 Mzt) constitutes an equally valid representation. Provided the Nx K matrix His of full rank K, the state space representation can be uniquely identified by imposing semi-arbitrary restrictions on any K rows of the matrix; for instance, setting H’ 9 (IK H2′), where H2 is an unconstrained (N- K)xK matrix. The system (A.6) can be estimated by Kalman filtration methods discussed in Shumway and Stoffer (1982), Watson and Engle (1983), and Hamilton (1994).
The data vectoryt consists of 3-, 6-, and 12-month DM Eurodeposit rates, and 1-7 year swap rates. All instruments maturing after January 1, 1999 were excluded, resulting in total elimination of the 6-year swap rates that only became available in 1994. Eurodeposit rates were available over an extended 1977-1998 interval; swap rates only after June 24, 1991. However, Kalman filtration methods can cope relatively easily with mismatched data sets and missing data.
The system (A.6) was estimated using various choices of the number K of factors. The first three identifying restrictions were chosen successively to mimic the level, slope, and curvature term structure factors advocated by Litterman and Sheinkmann (1988) — albeit for the short-maturity Eurodeposit rates for which there was the most data. The fourth factor was chosen to mimic the slope of the term structure for longer maturities. As discussed above, these restrictions are arbitrary. Many of the factors exhibited near-unit root behavior. For instance, the single-factor model of the term structure had a weekly autocorrelation of .99772, reflecting high persistence in German interest rates. Consequently, a conditional Kalman filtration was estimated that included estimation of the initial state vector z0 as of December 27, 1976.